HBD Number Puzzle • Beeloo Printable Crafts and Activities for Kids - Free Printable

Let’s solve this puzzle step by step.

This is a special kind of number puzzle — like Sudoku, but with numbers 1 to 8 (instead of 1 to 9), and the grid is 8x8. The rules are:

- Each row must have numbers 1 to 8, no repeats.
- Each column must have numbers 1 to 8, no repeats.
- Each 2x4 block (there are 4 blocks across and 2 down) must also have numbers 1 to 8, no repeats.

We’ll fill in the empty cells one by one, using logic: if a number is missing in a row, column, or block, and only one spot can take it, we put it there.

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Let’s label rows 1 to 8 from top to bottom, and columns 1 to 8 from left to right.

Start with Row 1:
[ ?, 3, ?, ?, 4, ?, 7, ? ]

Missing numbers: 1,2,5,6,8

Look at Column 1: has 5,6,4,?,8,7 → so missing 1,2,3 — but 3 is already in row 1, so for cell (1,1), possible: 1,2

But let’s look at Block 1 (top-left 2x4: rows 1–2, cols 1–4):

Row 1: [?,3,?,?]
Row 2: [?,4,1,6]
So current numbers in block: 3,4,1,6 → missing: 2,5,7,8

Cell (1,1): can’t be 3,4,1,6 → and from column 1, can’t be 5,6,4,8,7 → wait, column 1 has: row3=5, row4=6, row5=4, row7=8, row8=7 → so column 1 has: 5,6,4,8,7 → missing 1,2,3

But row 1 already has 3 → so (1,1) can be 1 or 2.

In block 1, missing 2,5,7,8 — so (1,1) could be 2 (since 1 is already in block? Wait, row2 col3 is 1 → yes, 1 is in block → so (1,1) cannot be 1 → must be 2!

✔ So (1,1) = 2

Now Row 1: [2,3,?,?,4,?,7,?]

Missing: 1,5,6,8

Column 3: has 1,3,4,?,8,7,5 → let’s list column 3:

Row2:1, Row3:3, Row4:4, Row5:?, Row6:8, Row7:7, Row8:5 → so values: 1,3,4,8,7,5 → missing 2,6

But row1 col3: can’t be 2 (already in row), so must be 6? Wait, 2 is not in column 3 yet? Column 3 has: 1,3,4,8,7,5 → missing 2,6

Row1 already has 2 → so (1,3) can be 6.

Also, in block 1, we have now: row1: 2,3,?,?; row2: ?,4,1,6 → so far: 2,3,4,1,6 → missing 5,7,8

(1,3) is in block 1 → can be 5,7,8 — but column 3 says only 2 or 6 allowed → conflict? Wait, I think I made a mistake.

Wait — column 3:

Let me write all known values in column 3:

Row1: ?

Row2: 1

Row3: 3

Row4: 4

Row5: ?

Row6: 8

Row7: 7

Row8: 5

So present: 1,3,4,8,7,5 → missing: 2,6

Yes.

Row1 already has 2 (we just placed it) → so (1,3) cannot be 2 → must be 6.

And 6 is not in block 1 yet? Block 1: row1: 2,3,6,? ; row2: ?,4,1,6 → oh! row2 col4 is 6 → so 6 is already in block 1 → conflict!

Oh no! That means my earlier assumption might be wrong.

Wait — row2 col4 is 6 → yes, so block 1 already has 6 → so (1,3) cannot be 6.

But column 3 requires (1,3) to be 2 or 6 → and row1 already has 2 → so no option? That can't be.

I think I messed up the block definition.

The puzzle says “block” — looking at the grid, the thick lines divide it into 4 blocks horizontally and 2 vertically? Let me check the image description.

Actually, in standard 8x8 Sudoku variants, blocks are usually 2x4 or 4x2. Looking at the grid, the bold lines are after every 2 rows and every 4 columns? Let me see:

From the grid layout:

Rows 1-2 are together, then 3-4, etc.? No — actually, looking at the original problem, the thick borders are around 2-row high and 4-column wide blocks? Let me count.

Actually, in the image, the grid is divided into 4 blocks across (each 2 columns wide?) — no, wait, 8 columns, so likely 4 blocks of 2 columns each? But that would be 2x8 blocks? That doesn’t make sense.

Standard for 8x8 is often 2x4 blocks. Let me assume blocks are 2 rows by 4 columns.

So:

Block 1: rows 1-2, cols 1-4

Block 2: rows 1-2, cols 5-8

Block 3: rows 3-4, cols 1-4

Block 4: rows 3-4, cols 5-8

Block 5: rows 5-6, cols 1-4

Block 6: rows 5-6, cols 5-8

Block 7: rows 7-8, cols 1-4

Block 8: rows 7-8, cols 5-8

Yes, that makes sense.

So back to row1 col3.

Block 1: rows 1-2, cols 1-4

Current values:

Row1: col1=?, col2=3, col3=?, col4=?

Row2: col1=?, col2=4, col3=1, col4=6

So known: 3,4,1,6

Missing in block: 2,5,7,8

Column 3: as before, has row2=1, row3=3, row4=4, row6=8, row7=7, row8=5 → so 1,3,4,8,7,5 → missing 2,6

Row1 has col1=2 (we thought), but let's verify that again.

Earlier I said (1,1) must be 2 because column 1 has 5,6,4,8,7 and row1 has 3, so only 1,2 possible, and block has 1 already (row2 col3), so (1,1)=2.

Is 1 in block 1? Yes, row2 col3=1.

So (1,1) cannot be 1, must be 2. OK.

So row1 col1=2.

Then row1: [2,3,?,?,4,?,7,?]

Column 3: missing 2,6 — but 2 is in row1, so (1,3) must be 6.

But is 6 allowed in block 1? Block 1 has row2 col4=6 — yes, so 6 is already in block 1 — conflict!

That means my block assumption is wrong.

Perhaps blocks are 4x2? Let me try that.

If blocks are 4 rows by 2 columns:

Block 1: rows 1-4, cols 1-2

Block 2: rows 1-4, cols 3-4

Block 3: rows 1-4, cols 5-6

Block 4: rows 1-4, cols 7-8

Block 5: rows 5-8, cols 1-2

etc.

Let me check if that works.

For example, in row2, cols 1-2: ?,4 — and row3 cols 1-2: 5,? — row4: 6,8 — so block 1 (rows1-4, cols1-2) would have: row1: ?,3; row2: ?,4; row3: 5,?; row4: 6,8 — so values: 3,4,5,6,8 — missing 1,2,7

That seems reasonable.

Similarly, block 2 (rows1-4, cols3-4): row1: ?,?; row2:1,6; row3:3,8; row4:4,7 — so 1,6,3,8,4,7 — missing 2,5

OK.

So probably blocks are 4x2.

I think I had it wrong initially. Let me confirm with the puzzle's instruction: "fill each row, column, and block" — and in the grid, the thick lines are after every 4 rows and every 2 columns? Looking at the image description, it's not clear, but typically for 8x8, it's 2x4 or 4x2.

To resolve the conflict, let's assume blocks are 4 rows by 2 columns, as that avoids the conflict.

So redefine:

Blocks are 4 rows high and 2 columns wide.

So:

- Block 1: rows 1-4, cols 1-2

- Block 2: rows 1-4, cols 3-4

- Block 3: rows 1-4, cols 5-6

- Block 4: rows 1-4, cols 7-8

- Block 5: rows 5-8, cols 1-2

- Block 6: rows 5-8, cols 3-4

- Block 7: rows 5-8, cols 5-6

- Block 8: rows 5-8, cols 7-8

Now, let's restart.

Row 1: [ ?, 3, ?, ?, 4, ?, 7, ? ]

Column 1: let's list all known in col1:

Row3:5, Row4:6, Row5:4, Row7:8, Row8:7 — so 5,6,4,8,7 — missing 1,2,3

Row1 has 3 in col2, so for (1,1), can be 1 or 2.

Block 1 (rows1-4, cols1-2):

Row1: ?,3

Row2: ?,4

Row3: 5,?

Row4: 6,8

So known values: 3,4,5,6,8 — missing 1,2,7

So (1,1) can be 1 or 2 (from column and row constraints).

No immediate conflict.

Let's look at row 8, which is almost full: [7,6,5,1,2,4,8,3] — all filled, good.

Row 7: [8, ?, 7, ?, ?, 1, 4, 6]

Missing: 2,3,5

Column 2: has row1:3, row2:4, row4:8, row6:5, row8:6 — so 3,4,8,5,6 — missing 1,2,7

Row7 col2: can be 2 (since 1 and 7 may be blocked).

Block 5 (rows5-8, cols1-2):

Row5:4,?

Row6:?,5

Row7:8,?

Row8:7,6

So known: 4,5,8,7,6 — missing 1,2,3

So (7,2) can be 2 or 3 (since 1 might be used).

Row7 missing 2,3,5 — and col2 missing 1,2,7 — so intersection: 2 is common.

Also, in block 5, missing 1,2,3 — so 2 is possible.

Let's see if 2 is forced.

Suppose (7,2) = 2.

Then row7: [8,2,7,?,?,1,4,6] — missing 3,5 for cols4 and5.

Col4: let's see what's there.

Col4: row2:6, row3:8, row4:7, row5:2, row6:4, row8:1 — so 6,8,7,2,4,1 — missing 3,5

Perfect! So (7,4) and (7,5) need to be 3 and 5.

Col4 missing 3,5 — col5: row1:4, row2:7, row3:1, row4:3, row5:8, row6:6, row8:2 — so 4,7,1,3,8,6,2 — missing 5

Col5 has only 5 missing? Let's list:

Row1:4

Row2:7

Row3:1

Row4:3

Row5:8

Row6:6

Row7:?

Row8:2

So values: 4,7,1,3,8,6,2 — missing 5

Yes! So (7,5) must be 5.

Then (7,4) must be 3 (since row7 missing 3 and 5, and col5 takes 5).

So (7,4)=3, (7,5)=5.

Now row7: [8,2,7,3,5,1,4,6] — complete.

Great.

Now update.

Back to row1.

We have (7,2)=2, so in column 2, we have: row1:3, row2:4, row4:8, row6:5, row7:2, row8:6 — so 3,4,8,5,2,6 — missing 1,7

Row1 col2 is 3, so for other cells in col2.

Now row1: [ ?,3,?,?,4,?,7,? ]

Missing: 1,2,5,6,8 — but 2 is now in col2 row7, but that's fine.

Column 1: still missing 1,2,3 — but row1 has 3, so (1,1) can be 1 or 2.

Block 1 (rows1-4, cols1-2): known: row1:?,3; row2:?,4; row3:5,?; row4:6,8 — so values: 3,4,5,6,8 — missing 1,2,7

So (1,1) can be 1 or 2.

Let's look at row2: [ ?,4,1,6,7,8,?,? ]

Missing: 2,3,5

Column 1: missing 1,2,3 — row2 col1 can be 2 or 3 (since 1 is in row2 col3).

Block 1: missing 1,2,7 — so (2,1) can be 2 or 7, but row2 has 7 in col5, so not 7 — so (2,1) can be 2.

Also, column 1 allows 2.

So perhaps (2,1)=2.

Then row2: [2,4,1,6,7,8,?,?] — missing 3,5 for cols7 and8.

Column 7: row1:7, row3:6, row4:1, row5:5, row7:4, row8:8 — so 7,6,1,5,4,8 — missing 2,3

Row2 col7 can be 3 (since 2 is used in row2).

Column 8: row3:4, row4:2, row6:1, row7:6, row8:3 — so 4,2,1,6,3 — missing 5,7,8

Row2 col8 can be 5.

So (2,7)=3, (2,8)=5.

Row2 complete: [2,4,1,6,7,8,3,5]

Good.

Now block 1: rows1-4, cols1-2: row1:?,3; row2:2,4; row3:5,?; row4:6,8 — so values: 3,2,4,5,6,8 — missing 1,7

So (1,1) and (3,2) need to be 1 and 7.

Column 1: missing 1,3 (since we have row2:2, row3:5, row4:6, row5:4, row7:8, row8:7 — so 2,5,6,4,8,7 — missing 1,3)

Row1 col1: can be 1 or 3, but row1 has 3 in col2, so must be 1.

Then (1,1)=1.

Then in block 1, (3,2) must be 7.

So (3,2)=7.

Now row3: [5,7,3,8,1,?,6,4] — missing only col6.

Row3: 5,7,3,8,1,?,6,4 — so missing 2.

Col6: let's see what's there.

Col6: row2:8, row4:? , row5:3, row6:? , row7:1, row8:4 — and row3:?

Known: 8,3,1,4 — missing many.

But row3 needs 2, so (3,6)=2.

Check if allowed: col6 has no 2 yet? Row4 col6 is empty, etc. Probably ok.

So (3,6)=2.

Row3 complete: [5,7,3,8,1,2,6,4]

Now row4: [6,8,4,7,3,?,1,2] — missing col6.

Values: 6,8,4,7,3,?,1,2 — missing 5.

So (4,6)=5.

Col6: now has row3:2, row4:5, row5:3, row7:1, row8:4 — and row2:8 — so 2,5,3,1,4,8 — missing 6,7

Ok.

Row4 complete: [6,8,4,7,3,5,1,2]

Now row1: [1,3,?,?,4,?,7,?]

Missing: 2,5,6,8

Column 3: row2:1, row3:3, row4:4, row6:8, row7:7, row8:5 — so 1,3,4,8,7,5 — missing 2,6

Row1 col3: can be 2 or 6.

Block 2 (rows1-4, cols3-4): row1:?,?; row2:1,6; row3:3,8; row4:4,7 — so 1,6,3,8,4,7 — missing 2,5

So (1,3) and (1,4) need to be 2 and 5.

But column 3 requires 2 or 6 — so (1,3) must be 2 (since 6 not in missing for block).

Then (1,4) must be 5.

So (1,3)=2, (1,4)=5.

Now row1: [1,3,2,5,4,?,7,?] — missing 6,8 for cols6 and8.

Column 6: missing 6,7 (as above: has 8,2,5,3,1,4 — so missing 6,7)

Row1 col6 can be 6 or 8, but col6 missing 6,7 — so must be 6.

Then (1,6)=6.

Then (1,8)=8.

Row1 complete: [1,3,2,5,4,6,7,8]

Now row5: [4,?,?,2,8,3,5,?]

Missing: 1,6,7

Column 2: has row1:3, row2:4, row3:7, row4:8, row6:5, row7:2, row8:6 — so 3,4,7,8,5,2,6 — missing 1

So (5,2) must be 1.

Then row5: [4,1,?,2,8,3,5,?] — missing 6,7 for cols3 and8.

Column 3: has row1:2, row2:1, row3:3, row4:4, row6:8, row7:7, row8:5 — so 2,1,3,4,8,7,5 — missing 6

So (5,3) must be 6.

Then (5,8) must be 7.

Row5 complete: [4,1,6,2,8,3,5,7]

Now row6: [?,5,8,4,6,?,?,1]

Missing: 2,3,7

Column 1: has row1:1, row2:2, row3:5, row4:6, row5:4, row7:8, row8:7 — so 1,2,5,6,4,8,7 — missing 3

So (6,1) must be 3.

Then row6: [3,5,8,4,6,?,?,1] — missing 2,7 for cols6 and7.

Column 6: has row1:6, row2:8, row3:2, row4:5, row5:3, row7:1, row8:4 — so 6,8,2,5,3,1,4 — missing 7

So (6,6) must be 7.

Then (6,7) must be 2.

Row6 complete: [3,5,8,4,6,7,2,1]

Now all rows are filled except we have row7 and8 done, row1-6 done.

Let me list the full grid:

Row1: 1,3,2,5,4,6,7,8

Row2: 2,4,1,6,7,8,3,5

Row3: 5,7,3,8,1,2,6,4

Row4: 6,8,4,7,3,5,1,2

Row5: 4,1,6,2,8,3,5,7

Row6: 3,5,8,4,6,7,2,1

Row7: 8,2,7,3,5,1,4,6

Row8: 7,6,5,1,2,4,8,3

Now verify if all rows have 1-8 unique: yes, each row has all different.

Columns:

Col1: 1,2,5,6,4,3,8,7 — all unique.

Col2: 3,4,7,8,1,5,2,6 — good.

Col3: 2,1,3,4,6,8,7,5 — good.

Col4: 5,6,8,7,2,4,3,1 — good.

Col5: 4,7,1,3,8,6,5,2 — good.

Col6: 6,8,2,5,3,7,1,4 — good.

Col7: 7,3,6,1,5,2,4,8 — good.

Col8: 8,5,4,2,7,1,6,3 — good.

Now blocks (4x2):

Block1 (r1-4,c1-2): r1:1,3; r2:2,4; r3:5,7; r4:6,8 → 1,3,2,4,5,7,6,8 — all unique.

Block2 (r1-4,c3-4): r1:2,5; r2:1,6; r3:3,8; r4:4,7 → 2,5,1,6,3,8,4,7 — good.

Block3 (r1-4,c5-6): r1:4,6; r2:7,8; r3:1,2; r4:3,5 → 4,6,7,8,1,2,3,5 — good.

Block4 (r1-4,c7-8): r1:7,8; r2:3,5; r3:6,4; r4:1,2 → 7,8,3,5,6,4,1,2 — good.

Block5 (r5-8,c1-2): r5:4,1; r6:3,5; r7:8,2; r8:7,6 → 4,1,3,5,8,2,7,6 — good.

Block6 (r5-8,c3-4): r5:6,2; r6:8,4; r7:7,3; r8:5,1 → 6,2,8,4,7,3,5,1 — good.

Block7 (r5-8,c5-6): r5:8,3; r6:6,7; r7:5,1; r8:2,4 → 8,3,6,7,5,1,2,4 — good.

Block8 (r5-8,c7-8): r5:5,7; r6:2,1; r7:4,6; r8:8,3 → 5,7,2,1,4,6,8,3 — good.

Perfect! All constraints satisfied.

So the completed puzzle is:

Row 1: 1, 3, 2, 5, 4, 6, 7, 8
Row 2: 2, 4, 1, 6, 7, 8, 3, 5
Row 3: 5, 7, 3, 8, 1, 2, 6, 4
Row 4: 6, 8, 4, 7, 3, 5, 1, 2
Row 5: 4, 1, 6, 2, 8, 3, 5, 7
Row 6: 3, 5, 8, 4, 6, 7, 2, 1
Row 7: 8, 2, 7, 3, 5, 1, 4, 6
Row 8: 7, 6, 5, 1, 2, 4, 8, 3

Final Answer:
The completed grid is:
1 3 2 5 4 6 7 8
2 4 1 6 7 8 3 5
5 7 3 8 1 2 6 4
6 8 4 7 3 5 1 2
4 1 6 2 8 3 5 7
3 5 8 4 6 7 2 1
8 2 7 3 5 1 4 6
7 6 5 1 2 4 8 3